This invention relates in general to a system and method for nonlinear frequency conversion tunable laser light using achromatic phase-matching, and in particular to an achromatic phase-matching optical system and method which exactly matches the high order dispersion characteristics of nonlinear optical materials.
Many applications require broadly tunable UV light. No such laser source exists, however, so tunable UV is usually obtained by frequency-doubling a tunable laser in the visible and near-IR by using nonlinear optical effects such as a second harmonic generation process. Such processes are phenomenon which derive from nonlinear polarization effects of certain material media. The effect depends upon crystal structure, particularly anisotropic structure. Commonly used crystals are xcex2-barium borate (xe2x80x9cBBOxe2x80x9d), potassium dihydrogen phosphate (xe2x80x9cKDPxe2x80x9d) and lithium triborate (xe2x80x9cLBOxe2x80x9d).
Because frequency-doubling, therefore, involves passing light through a nonlinear crystal, the effects of its wavelength-dependent refractive index must be taken into account. In particular, in order for frequency doubling to take place in the crystal, the refractive index of the incident light at the xe2x80x9cfundamentalxe2x80x9d wavelength and with its polarization must equal the refractive index of the frequency doubled light (with its own polarization) to be produced. Since the refractive index of the crystal varies both with the angle of incidence and with the frequency of the input beam it is apparent the that absent extraordinary precaution only a very narrow range of frequencies of a broadband beam can enter a crystal at the appropriate incident angle for efficient frequency doubling.
Second-harmonic generation of light (hereafter referred to as xe2x80x9cSHGxe2x80x9d) the generation of light of twice the optical frequency of input laser light, has been an essential tool of laser research for many years. It is used widely to generate ultraviolet light because such wavelengths are difficult to generate directly from a laser. Indeed, this technique is often used to generate visible light from a near-infrared laser because it is easier to generate near-infrared laser light than it is to generate visible light. In general, however, it is possible to frequency-double light from virtually all visible and near-infrared lasers.
A particular type of laser light which is important to frequency-double is broadband light. However, the use of SHG processes to frequency-double broadband light which is incoherent has proved to be difficult and inefficient. (In general, ultrashort pulses generated by lasers can be considered broadband light whose frequencies are in phase while incoherent light can be considered broadband light whose frequencies are randomly phased.) These two types of light are difficult to frequency-double due to their respective large bandwidths. As a result of the large bandwidths, efficient methods for frequency-doubling both of these types of light have not been developed.
The efficiency xcex7 of a SHG process depends on several factors. A first factor is the nonlinear coefficient of the SHG crystal used. This factor depends on internal properties of the crystal and can only be improved by manipulating the composition of the crystal.
Second, xcex7 is proportional to the square of the length of the crystal, L, the distance through which light ray propagate through the crystal. Thus, thick crystals yield much higher efficiency than thin ones.
Third, xcex7 depends on the laser intensity and is, typically, directly proportional to the laser intensity. Consequently, continuous-beam lasers, which have relatively low intensity, frequency-double inefficiently while pulsed lasers, which generally achieve higher intensity, frequency-double more efficiently. In general, the shorter the pulse the more efficiently it frequency-doubles, given a fixed energy per pulse.
As earlier noted, in order for frequency-doubling to take place in an SHG crystal, the refractive index of the input laser light (again, the xe2x80x9cfundamentalxe2x80x9d wavelength) must equal the refractive index of the frequency-doubled light to be produced. Since the refractive index of a crystal is a function of both the incidence angle and frequency of the input beam different incidence angles must be used to obtain maximum efficiency xcex7 for different wavelengths. The requirement that a wavelength enter the crystal at the appropriate angle necessary to frequency-double most efficiently will be referred to hereinafter as the xe2x80x9cphase-matching condition,xe2x80x9d or simply xe2x80x9cphase-matchingxe2x80x9d for short. The angle will be referred to as the xe2x80x9cphase-matching angle,xe2x80x9d and is a function of wavelength.
Because the efficiency xcex7 of the SHG process is strongly xe2x80x9cpeakedxe2x80x9d with respect to the entrance angle for a given wavelength and also with respect to wavelength for a given angle, only a very narrow range of wavelengths near the exact phase-matching wavelength can yield highly efficient SHG process. The range of wavelengths that achieves high-efficiency frequency-doubling for a single angle is called the crystal""s xe2x80x9cphase-matching bandwidthxe2x80x9d for that angle. If the input laser light contains frequencies outside this bandwidth, such frequencies will not produce their corresponding second harmonic (i.e., will not be frequency-doubled) and the efficiency of the overall process is reduced.
When the crystal bandwidth is greater than the input light bandwidth, the above effect can be neglected. However, when the crystal bandwidth is less than the bandwidth of the input light, the SHG efficiency is proportional to the crystal bandwidth, yielding a fourth factor. In this case, the efficiency can be written approximately as:   η  ∝            d      2        xc3x97    l    xc3x97                  L        2            ⁢              (                              Δ            ⁢                          xe2x80x83                        ⁢                          λ              cr                                            Δ            ⁢                          xe2x80x83                        ⁢                          λ              l                                      )            
where d is the nonlinear coefficient of the crystal, l is the intensity of the light, L is the length of the crystal through which the light propagates, xcex94xcexcr is the bandwidth of the crystal, and xcex94xcexl is the bandwidth of the incident light. Furthermore, the bandwidth, xcex94xcexcr, of an SHG crystal is given by:       Δ    ⁢          xe2x80x83        ⁢          λ      cr        =            λ              4        ⁢        l                                      (                                    ⅆ              n                                      ⅆ              λ                                )                f            -                        (                                    ⅆ              n                                      ⅆ              λ                                )                s            
where xcex is the wavelength of light and dn/dxcex is the derivative of the refractive index n with respect to wavelength at the appropriate polarization of the fundamental wavelength and second harmonic wavelength, indicated by the subscripts, f and s, respectively.
Thus, the bandwidth of an SHG crystal is a function of the crystal""s refractive-index vs. wavelength curve: a fundamental property of the crystal. Furthermore, the bandwidth is inversely proportional to the crystal length. Hence, if one attempts to increase the conversion efficiency by increasing the crystal length, one must also increase the precision of the phase-matching thereby reducing the tolerance for error in the entrance angle of the incoming beam.
Various attempts to improve the efficiency of the SHG process have been and continue to be made. Several researchers have introduced achromatic phase-matching (APM) devices that use angular dispersion so that each wavelength enters the nonlinear crystal at its appropriate phase-matching angle as a way of increasing the bandwidth of the crystal and therefore, increase its efficiency. The crystal and all dispersing optics remain fixed. Because such systems have no moving parts, they are inherently instantaneously tunable, and can be used for nonlinear conversion of tunable or broadband (such as ultrashort) radiation. Most of these devices have used diffraction gratings or prisms in combination with lenses which are sensitive to translational misalignment. Also, previous work has considered only the lowest order (linear) term of the media-created dispersion and the phase-matching angle tuning function. Bandwidths of about 10 times the natural bandwidth of the crystal were achieved; larger bandwidths were only obtained by using a divergent beam at the expense of conversion efficiency.
In order to obviate these shortcomings, therefore, a system using a unique arrangement of prisms was provided which achieved sufficient angular dispersion to allow bringing an approximately 100 nm bandwidth of light into proper alignment in a nonlinear media for SHG by matching the first two orders of the spatial dispersion angle as a function of wavelength from approximately 610 nm to 710 nm wavelength. The relationship between the phase-matching angle and the wavelength xcex was approximated by modeling an angularly dispersive optical system such that the dispersion angles of the light propagating through that system, as a function of the wavelengths, match the phase-matching angles of the SHG crystal, again as a function of wavelength, in both the first and the second order terms of the polynomials describing the light dispersion angle and the phase-matching angle. In doing so, it is possible to bring a much broader band of light wavelengths into the SHG crystal at the optimum angles for frequency doubling. Such a system is described and shown in prior co-pending application Ser. No. 09/187,721. And is herein incorporated by reference.
However, this so-called second order system is large and complex and provides temporal dispersion control only with difficulty. What is needed, therefore, is a more compact apparatus which can provide the same or greater spatial dispersion together with temporal dispersion control.
It is therefore an object of this invention to provide a compact optical system for performing achromatic phase-matching by matching the dispersion angles of input rays/beams to the phase-matching angles of those rays/beams in a nonlinear medium while also providing control of the temporal dispersion of the input rays/beams.
It is another object to provide an achromatic phase-matching optical system, for use in a SHG process, having elements configured to very closely match the first three order s of the angular dispersion of the phase-matching angle of the SHG crystal such that the angular dispersion at all incident frequencies of a broadband pulse of light (or tunable) passing through the elements is such that each given frequency enters the SHG crystal sufficiently close to its exact phase-matching angle that nonlinear conversion is efficient.
To achieve these and other objects, there is provided an apparatus and method for efficiently converting a large bandwidth light pulse into a similarly large bandwidth pulse of light whose frequency is a multiple of its original incoming frequency by means of a nonlinear optical medium. If the nonlinear responding medium is a SHG crystal, the light beam incident upon the crystal is passed though the crystal and is frequency-doubled. It should be noted, however, that the instant invention is not limited solely to frequency doubling nonlinear responses.